ACT Math: Trigonometry Drill 5, Problem 4. What is the measure of the angle?
|Foreign Language||Arabic Subtitled|
|Geometry||Right Triangles and Trigonometry|
|Product Type||ACT Math|
|Trigonometry||SOHCAHTOA (values and properties of trig functions)|
Solving right triangles
Trigonometric relations in right triangles
Remember your triangle trig ratios?
Tangent is opposite over adjacent.
The ratio of the opposite side of the angle x over the adjacent side to x is the square root of
3 or root 3 over 1. Okay. Pythagorean Theorem time!
One squared plus root three squared equals the hypotenuse squared. One plus three equals
the hypotenuse squared... so four equals the hypotenuse squared.
Take the square root of both sides, and we get that the hypotenuse equals 2.
The ratio of the sides is 1 to √3 to 2, which means this is a special triangle.
It's a 30-60-90 triangle, and x, the angle opposite the second longest side is the second
largest angle, which makes it 60 degrees. Option D is the correct answer.